Multiphase flows are ubiquitous is Nature and industrial processes. Rain, breaking waves, sprays, bubbly flows, and boiling, are only a few examples. Accurately predicting the behavior of such flows is critical for the air-ocean exchange of heat and mass in climate modeling, for atomization and clean combustion of liquid fuels, for heat transfer in conventional and nuclear power plants, for selectivity in chemical reactions in bubble columns, and many other systems of immerse economic importance. In many cases the flow is well described by continuum theories (the Navier-Stokes equations) but the range of scales for the systems that we are interested in is so large that averaged or reduced order models are used for predictions of realistic systems. Such modes generally include terms that are not known and need to be related to the model variables thorugh closure relations.

Direct Numerical Simulations (or DNS), where fully resolved numerical simulations of systems that are small enough so that all continuum length and time-scales can be fully resolved, but large enough for non-trivial scale interactions to take place, are used to examine the dynamics of well-defined multiphase systems offer the best way to develop closure models for industrial models.

The members of the Computational Multiphase Group have pioneered DNS of multiphase flows, starting with the development of a versatile and numerical method in the late eighties and early nineties. The method combines a relatively standard finite volume flow solver with a front tracking method, where connected marker points are used to track the boundary between the different fluids. The method, with many improvements and extensions, has now been used to examine a range of problems, including bubbles in initially quiescent flows, bubbles in turbulent channel flows, suspensions of drops, collision of drops, electrohydrodynamics of droplet suspensions, thermocapillary migration of bubbles and drops, effect of surfactants on bubble motion, solidification, boiling and many other problems.

We are currently engaged in several studies that address two kinds of questions. What do we do with the results and how do we simulate complex multiphysics and multiscale problems.

For many flows, such as bubbly flows, DNS are now possible for relatively large systems such as hundreds of bubbles in turbulent flows and for a long enough time so that reliable statistical results can be gathered. One of the central question for such systems is the existence of lower order description, either because such descriotions can be used to explain the dynamics or because it can lead to models that can be used to predict the behavior of industrial systems where DNS is impractical. Such models can take several forms, including Two-Fluid models for the average flow and filtered LES like models for the large scale flow. In both cases the averaging/filtering results in unknown closure terms that need to be correlated with known quantities. We are currently exploring various ways to process the DNS date, including using machine learning to find important relationships in the data.

Many natural multiphase problems exhibit a large range of temporal and spatial scales, either because dynamic processes lead to their generations, such as thin films and filaments and tiny drops, or because of the presence of different physical effects that take place on very different timecale, such as mass transfer and reactions in unsteady fluid flow. While adaptive grid refinement is, in principle, able to resolve such processes, the large range scales still results in excessive number of grid points. In many cases the small scale motion is dominated by surface tension and viscosity, resulting in a relatively simple geometry and simple flows that can be described or approximated analytically. We have develop methods to embed such small scale features in simulations of the larger scale motion using semi-analytical description that are solved along with the rest of the computations.